1. Field of the Invention
The present invention relates to an automatic pipe gridding method allowing implementation of codes for modelling fluids carried by these pipes.
2. Description of the Prior Art
The modes of flow of multiphase fluids in pipes are extremely varied and complex. Two-phase flows, for example, can be stratified, the liquid phase flowing in the lower part of the pipe, or intermittent with a succession of liquid and gaseous plugs, or dispersed, the liquid being carried along as fine droplets. The flow modes vary notably with the inclination of the pipes in relation to the horizontal and it depends on the flow rate of the gas phase, on the temperature, etc. Slippage between the phases, which varies according to whether the ascending or the descending pipe sections are considered, leads to pressure variations without there being necessarily any compensation. The characteristics of the flow network (dimensions, pressure, gas flow rate, etc.) must be carefully determined.
The TACITE simulation code takes into account a certain number of parameters that directly influence the physics of the problem which is considered. Examples of these parameters are the properties of the fluids and of the flow modes, the topographic variations (length, inclination, diameter variations, etc.), the possible roughness of the pipes, their thermal properties (number of insulating layers and their nature), or the arrangement of equipments along the pipe (pumps, injectors, separators, etc.) that lead to physical flow changes.
Gridding of a physical domain is an essential stage within the scope of numerical simulation. The validity of the results and the calculating times depend on the quality thereof. It is therefore fundamental to provide the code with a correct grid prior to starting simulation. The quality of a grid is generally judged from its capacity to properly describe physical phenomena without simulation taking up too much time, so that there always is an optimum grid for each problem studied. An unsuitable grid can lead, during implementation of the numerical pattern that governs the simulation, to errors that are difficult to detect, at least initially, and can even make calculation impossible and stop the execution of the code if it is excessively aberrant. Code users are not necessarily experienced enough in numerical analysis to produce a correct grid likely to really take into account the physical phenomena to be studied.
The topography of a cylindrical pipe can be compared to a succession of segments of lines connecting successive points. In cartesian coordinates, two successive points of the pipe on the vertical (ascending or descending) portions thereof can have the same abscissa (curve A in FIG. 1). It is therefore preferable to represent the elevation of each point as a function of its curvilinear abscissa along the pipe. With this mode of representation, successive points of the pipe of different elevations necessarily have two distinct curvilinear abscissas and the slope of the pipe sections is at most 45° to the horizontal (case of absolutely vertical ascending or descending sections, the curve in FIG. 1). One ordinate and only one always corresponds to an abscissa.
With some physical sense, certain gridding errors can be prevented. A finer grid pattern can be imposed in places of the pipe likely to undergo great physical parameter variations if they can be foreseen. Less calculations are thus carried out in each time interval while keeping the desired fineness in the important places. However, going from a fine cell to a coarser cell must be continuous with a view to obtaining a continuous solution.
FIG. 2a shows for example a 2-km long W-shaped pipe section comprising four 500-m long section. If such a pipe is discretized with cells having a constant 40-m interval from beginning to end, the important points of the route at 500 m and 1500 m are left out. The simulation will not allow correctly showing the accumulation of liquid at these lower points of the topography. More important yet, the calculation is distorted by the fact that the angles of the W are replaced by horizontal segments of lines (FIG. 2b). The physical phenomena observed are thus not the phenomena that are sought.
The method according to the invention allows obtaining automatic gridding or discretization of a pipe taking into account, in the best possible way, the topography and the physical parameters that affect the flow physics, subjected to the following constraints:                1—Ensure calculation convergence;        2—Best represent large accumulations of liquid at the lower points of the pipe;        3—Place the equipments on a cell edge;        4—Impose the same order of length on two consecutive cells;        5—Respect the total length of the pipe;        6—Limit the number of cells to the possible minimum by respecting the previous constraints so as not to penalize simulation with the calculating time.        
Respecting the previous six constraints is not easy, but it is essential in order not to grid the pipe studied homogeneously, without having to care about the physics of the problem, like most automatic gridders do.
In order to limit the number of cells, one has to try to simplify, if possible, the topography in order to keep only the zones of the pipe where the significant profile variations likely to significantly influence the physical phenomena are present.